qpms/besseltransforms/ksmall/5-3-2

(-5*(((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/(3*k^2)) + 10*(((-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/(3*k^2)) - 10*(((-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2)) + 5*(((-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/(3*k^2)) - ((-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0))/6 - ((-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^2) + I/6*(3*k0 - (2*k0^3)/k^2 - 2*Sqrt[-k^2 + k0^2] + (2*k0^2*Sqrt[-k^2 + k0^2])/k^2))/k0^3
(-5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - ((-3 + 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0))/6. - ((-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3))/(3.*Power(k,2)) + Complex(0,0.16666666666666666)*(3*k0 - (2*Power(k0,3))/Power(k,2) - 2*Sqrt(-Power(k,2) + Power(k0,2)) + (2*Power(k0,2)*Sqrt(-Power(k,2) + Power(k0,2)))/Power(k,2)))/Power(k0,3)
SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1]
(5*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 5*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + I*(k^2*(3*k0 - 2*Sqrt[-k^2 + k0^2]) + 2*k0^2*(-k0 + Sqrt[-k^2 + k0^2])))/(6*k^2*k0^3)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-5(((-3 + 2Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3)/(3k^2)) + 10(((-3 + 2Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3)/(3k^2)) - 10(((-3 + 2Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3)/(3k^2)) + 5(((-3 + 2Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3)/(3k^2)) - ((-3 + 2Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0))/6 - ((-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3)/(3k^2) + I/6(3k0 - (2k0^3)/k^2 - 2Sqrt[-k^2 + k0^2] + (2k0^2Sqrt[-k^2 + k0^2])/k^2))/k0^3
			(-5(((-3 + 2Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))(c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,3))/(3.Power(k,2))) + 10(((-3 + 2Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))(2c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,3))/(3.Power(k,2))) - 10(((-3 + 2Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))(3c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,3))/(3.Power(k,2))) + 5(((-3 + 2Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))(4c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,3))/(3.Power(k,2))) - ((-3 + 2Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))(5c - Complex(0,1)k0))/6. - ((-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,3))/(3.Power(k,2)) + Complex(0,0.16666666666666666)(3k0 - (2Power(k0,3))/Power(k,2) - 2Sqrt(-Power(k,2) + Power(k0,2)) + (2Power(k0,2)Sqrt(-Power(k,2) + Power(k0,2)))/Power(k,2)))/Power(k0,3)
			`SeriesData[k, Infinity, {(75c^6)/(2k0^3) - ((15I)c^5)/k0^2, 0, (-105(75c^8 - (80I)c^7k0 - 30c^6k0^2 + (4I)c^5k0^3))/(8k0^3), 0, (315(2025c^10 - (3310I)c^9k0 - 2250c^8k0^2 + (800I)c^7k0^3 + 150c^6k0^4 - (12I)c^5k0^5))/(32*k0^3)}, 5, 11, 1]`
			(5k^2(3 - 2Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) - 10(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 10k^2(-3 + 2Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 20(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 10k^2(3 - 2Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) - 20(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 5k^2(-3 + 2Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 10(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + k^2(3 - 2Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) - 2(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + I(k^2(3k0 - 2Sqrt[-k^2 + k0^2]) + 2k0^2(-k0 + Sqrt[-k^2 + k0^2])))/(6k^2*k0^3)